Kenneth Kau, a recent graduate of the University of Hawai‘i–West O‘ahu, wrote an article published by one of the leading sources of knowledge for the world’s applied mathematics and computational science communities.
The Society for Industrial and Applied Mathematics (SIAM) Undergraduate Research Online (SIURO) journal published on Sept. 23 Kau’s article, “Predicting Market Share: Application of Alternative Lotka-Volterra Competition Model.”
SIAM is an international organization that was incorporated to convey useful mathematical knowledge to other professionals who could implement mathematical theory for practical, industrial, or scientific use, according to its website.
SIAM publishes 18 peer-reviewed research journals, including SIURO, a web-based publication that consists of articles written by undergraduate students in applied and computational mathematics, offering an opportunity for students to publish research they have completed as part of their undergraduate education and providing undergraduates incentives for conducting research, according to the site.
Kau’s paper introduces a fresh approach to understanding competition in the technology sector by applying a model traditionally used in ecology — the Lotka-Volterra system.
“The main question that the paper looks to answer is whether we can take a specific model used for modeling competition amongst two competing species — think rabbits versus deer competing for grass — and see if we can apply it to modeling competition among firms — Apple and Samsung competing for the smartphone market,” Kau said. “However, we also want to know if it can not only capture the competition dynamic but also provide additional insights about how the firms compete that aren’t immediately obvious.”
Originally developed to study species competition, the Lotka-Volterra system is used in Kau’s research to explore how tech firms interact and compete in the marketplace, said Dr. Esther Widiasih, UH West O‘ahu Professor of Mathematics and Kau’s project advisor.
“The study examines whether this model can accurately predict future market shares and align with current trends,” Widiasih said. “Additionally, it looks at how changes in competition dynamics might impact market outcomes. By drawing comparisons between ecological and economic competition, the paper offers valuable insights that could help shape market strategies. This research also opens the door for future studies, including more complex scenarios involving multiple firms and unpredictable factors.”
Standout ‘dedication and critical thinking’
Kau, born and raised on O‘ahu with Kanaka Maoli ancestry, graduated in spring 2022 from UH West O‘ahu with a Bachelor of Arts in Social Sciences with a concentration in Economics. Shortly after in July, he took a position as an economist with the United States Army Corps of Engineers (USACE) in Jacksonville, Fla.
“I returned to UH West O‘ahu to take math courses online in the fall after,” Kau said. “At the time, I didn’t necessarily know whether I wanted to do economics graduate school, but I wanted the option of it, and you need a lot of math.”
So Kau enrolled in post-baccalaureate courses — Applied Probability Theory in fall 2022, Linear Algebra and Differential Equations in spring 2023 (when the under-workings of his paper started as a class project), Ordinary Differential Equations and Stability Theory in fall 2023, and Real Analysis in spring 2024.
“As a student in my upper division class, Kenneth’s dedication and critical thinking stood out to me,” Widiasih said. “I pushed him further to write up his final project in the 400-level Differential Equations class as a publication, and send it to SIURO journal. The reviewers in this journal consist of faculty members of various institutions who are experts in their fields, but also care about undergraduate education. So, we know that the final product will have to be rigorous.”
Kau, who is now a first-year economics Ph.D. student at the University of Wyoming, shared that he “wasn’t always a good student,” even failing Algebra 2 in high school.
“The point I want to make is that it is never too late to turn your academics around,” Kau emphasized. “I wish I had taken school seriously earlier on because it really can open a lot of cool opportunities.”
Kau credits several people with helping him throughout his academic journey: his girlfriend, family, and UH West O‘ahu professors Widiasih, Dr. Thomas Scheiding, Dr. Michael Furuto, and Dr. Katherine Aumer.
Kau said he also received a great deal of support from his former colleagues at USACE in Florida and from numerous officers and non-commissioned officers from his time in the U.S. Army Reserve, specifically with the 100th Battalion, 442nd Infantry in Fort Shafter.
“I cannot emphasize enough that I wouldn’t be where I am today without the support of these people,” he said.
Value of writing and publication process for students
Widiasih commented on the significance of Kau’s article being published in SIURO, noting that for students like Kau, engaging in the writing and publication process is super valuable because it builds essential skills in clear written communication, critical thinking, and in-depth research.
“In this process, students learn to organize and present complex ideas effectively, deepening their understanding, and ultimately, gaining confidence as emerging contributors,” Widiasih said. “This experience also teaches them to handle feedback through the manuscript review process. This will help them grow resilient and also, refine their work.”
For those students planning to go to graduate programs, where a dissertation or thesis is the norm, there are few other opportunities to learn the process of producing rigorous, high-quality work, Widiasih said.
“I would say that the significance of having the article published was proving to myself that I could handle conducting original work that is economics-related, mathematically rigorous, and able to meet journal standards,” Kau said. “Research is tough, and modeling is tough, but the ability to be a good communicator of your ideas is the most challenging aspect of all, in my opinion.”